Question: Reduce to lowest terms: $- \dfrac{7}{8} \div - \dfrac{3}{8} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{3}{8}$ is $- \dfrac{8}{3}$ Therefore: $ - \dfrac{7}{8} \div - \dfrac{3}{8} = - \dfrac{7}{8} \times - \dfrac{8}{3} $ $ \phantom{- \dfrac{7}{8} \times - \dfrac{8}{3}} = \dfrac{-7 \times -8}{8 \times 3} $ $ \phantom{- \dfrac{7}{8} \times - \dfrac{8}{3}} = \dfrac{56}{24} $ The numerator and denominator have a common divisor of $8$, so we can simplify: $ \dfrac{56}{24} = \dfrac{56 \div 8}{24 \div 8} = \dfrac{7}{3} $